Question 975581
{{{cos(2Z)=cos^2(Z)-sin^2(Z)}}}
{{{Z=sin^(-1)(x)}}}
In other words,
{{{sin(Z)=x}}}
By relation,
{{{cos^2(Z)+x^2=1}}}
{{{cos^2(Z)=1-x^2}}}
and
{{{sin^2(Z)=x^2}}}
Substituting,
{{{cos(2Z)=(1-x^2)-x^2}}}
{{{cos(2*sin^(-1)(x))=highlight(1-2x^2)}}}